#! /usr/bin/env python
# -*- coding: utf-8 -*-
#
# graph_tool -- a general graph manipulation python module
#
# Copyright (C) 2006-2026 Tiago de Paula Peixoto <tiago@skewed.de>
#
# This program is free software; you can redistribute it and/or modify it under
# the terms of the GNU Lesser General Public License as published by the Free
# Software Foundation; either version 3 of the License, or (at your option) any
# later version.
#
# This program is distributed in the hope that it will be useful, but WITHOUT
# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
# FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
# details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.

from .. import Graph, _get_rng, Vector_size_t, _parallel
from .. decorators import _limit_args
from . blockmodel import DictState, BlockState
from . base_states import *
from . partition_modes import contingency_graph

from .. dl_import import dl_import
dl_import("from . import libgraph_tool_inference as libinference")

import numpy as np
import math
from scipy.special import gammaln

@entropy_state_signature
class PartitionCentroidState(MCMCState, MultiflipMCMCState, MultilevelMCMCState,
                             GibbsMCMCState):
    r"""Obtain the center of a set of partitions, according to the variation of
    information metric or reduced mutual information.

    Parameters
    ----------
    bs : iterable of iterable of ``int``
        List of partitions.
    b : ``list`` or :class:`numpy.ndarray` (optional, default: ``None``)
        Initial partition. If not supplied, a partition into a single group will
        be used.
    RMI : ``bool`` (optional, default: ``False``)
         If ``True``, the reduced mutual information will be used, otherwise the
         variation of information metric will be used instead.
    """

    def __init__(self, bs, b=None, clabel=None, RMI=False):
        EntropyState.__init__(self)
        self.bs = bs = np.asarray(bs, dtype="int64")
        if b is None:
            b = np.zeros(bs.shape[1], dtype="int64")
        self.b = np.array(b, dtype="int64")
        if clabel is None:
            clabel = np.zeros(bs.shape[1], dtype="int64")
        self.clabel = np.asarray(clabel, dtype="int64")
        self.RMI = RMI
        self._state = libinference.make_partition_centroid_state(self)

    def get_B(self):
        r"Returns the total number of blocks."
        return len(np.unique(self.b))

    def get_Be(self):
        r"""Returns the effective number of blocks, defined as :math:`e^{H}`, with
        :math:`H=-\sum_r\frac{n_r}{N}\ln \frac{n_r}{N}`, where :math:`n_r` is
        the number of nodes in group r.
        """
        w = np.array(np.bincount(self.b), dtype="double")
        w = w[w>0]
        w /= w.sum()
        return np.exp(-(w*log(w)).sum())

    @copy_state_wrap
    def _entropy(self, **kwargs):
        r"""Return the description length (negative joint log-likelihood)."""
        return EntropyState._entropy_dispatch(**dict(locals(), **kwargs))


def variation_information(x, y, norm=False):
    r"""Returns the variation of information between two partitions.

    Parameters
    ----------
    x : iterable of ``int`` values
        First partition.
    y : iterable of ``int`` values
        Second partition.
    norm : (optional, default: ``False``)
        If ``True``, the result will be normalized in the range :math:`[0,1]`.

    Returns
    -------
    VI : ``float``
        Variation of information value.

    Notes
    -----

    The variation of information [meila_comparing_2003]_ is defined as

    .. math::

        \text{VI}(\boldsymbol x,\boldsymbol y) = -\frac{1}{N}\sum_{rs}m_{rs}\left[\ln\frac{m_{rs}}{n_r} + \ln\frac{m_{rs}}{n_s'}\right],

    with :math:`m_{rs}=\sum_i\delta_{x_i,r}\delta_{y_i,s}` being the contingency
    table between :math:`\boldsymbol x` and :math:`\boldsymbol y`, and
    :math:`n_r=\sum_sm_{rs}` and :math:`n'_s=\sum_rm_{rs}` are the group sizes
    in both partitions.

    If ``norm == True``, the normalized value is returned:

    .. math::

        \frac{\text{VI}(\boldsymbol x,\boldsymbol y)}{\ln N}

    which lies in the unit interval :math:`[0,1]`.

    This algorithm runs in time :math:`O(N)` where :math:`N` is
    the length of :math:`\boldsymbol x` and :math:`\boldsymbol y`.

    Examples
    --------
    >>> x = np.random.randint(0, 10, 1000)
    >>> y = np.random.randint(0, 10, 1000)
    >>> gt.variation_information(x, y)
    4.525389...

    References
    ----------
    .. [meila_comparing_2003] Marina Meilă, "Comparing Clusterings by the
       Variation of Information," in Learning Theory and Kernel Machines,
       Lecture Notes in Computer Science No. 2777, edited by Bernhard Schölkopf
       and Manfred K. Warmuth (Springer Berlin Heidelberg, 2003) pp. 173–187.
       :doi:`10.1007/978-3-540-45167-9_14`

    """
    g = contingency_graph(x, y)
    nr = g.degree_property_map("out", g.ep.mrs)
    nr = nr.fa[nr.fa > 0]
    mrs = g.ep.mrs.fa
    mrs = mrs[mrs > 0]
    N = mrs.sum()
    VI = -2 * (mrs * np.log(mrs)).sum() + (nr * np.log(nr)).sum()
    VI /= N
    if norm:
        VI /= np.log(N)
    return float(VI)

@_limit_args({"avg_method": ["min", "max", "arithmetic", "geometric"]})
def mutual_information(x, y, norm=False, adjusted=False, avg_method="arithmetic"):
    r"""Returns the mutual information between two partitions.

    Parameters
    ----------
    x : iterable of ``int`` values
        First partition.
    y : iterable of ``int`` values
        Second partition.
    norm : ``bool`` (optional, default: ``True``)
        If ``True``, the result will be normalized in the range :math:`[0,1]`.
    adjusted : ``bool`` (optional, default: ``False``)
        If ``True``, the adjusted mutual information will be computed. Note that
        if ``adjusted == True``, the parameter ``norm`` is ignored.
    avg_method : ``bool`` (optional, default: ``"arithmetic"``)
        Determines how the adjusted normalization average should be
        computed. Must be one of: ``"min"``, ``"max"``, ``"arithmethic"``, or
        ``"geometric"``. This option has an effect only if ``adjusted == True``.

    Returns
    -------
    MI : ``float``
        Mutual information value

    Notes
    -----

    The mutual information is defined as

    .. math::

        \text{MI}(\boldsymbol x,\boldsymbol y) = \frac{1}{N}\sum_{rs}m_{rs}\ln\frac{N m_{rs}}{n_rn'_s},

    with :math:`m_{rs}=\sum_i\delta_{x_i,r}\delta_{y_i,s}` being the contingency
    table between :math:`\boldsymbol x` and :math:`\boldsymbol y`, and
    :math:`n_r=\sum_sm_{rs}` and :math:`n'_s=\sum_rm_{rs}` are the group sizes
    in both partitions.

    If ``norm == True``, the normalized value is returned:

    .. math::

        2\frac{\text{MI}(\boldsymbol x,\boldsymbol y)}{H_x + H_y}

    which lies in the unit interval :math:`[0,1]`, and where :math:`H_x =
    -\frac{1}{N}\sum_rn_r\ln\frac{n_r}{N}` and :math:`H_x =
    -\frac{1}{N}\sum_rn'_r\ln\frac{n'_r}{N}`.

    If ``adjusted == True``, the adjusted mutual information is returned, defined
    as [vinh_information_2009]_:

    .. math::

       \text{AMI}(\boldsymbol x,\boldsymbol y) =
       \frac{\text{MI}(\boldsymbol x,\boldsymbol y) - E[\text{MI}(\boldsymbol x,\boldsymbol y)]}
       {\text{avg}(H_x, H_y) - E[\text{MI}(\boldsymbol x,\boldsymbol y)]},

    where

    .. math::

        E[\text{MI}(\boldsymbol x,\boldsymbol y)] =
        \sum_r\sum_s\sum_{m=\max(1,n_r+n'_s-N)}^{\min(n_r, n'_s)}
        \frac{m}{N} \ln \left( \frac{Nm}{n_rn'_s}\right) \times \\
        \frac{n_r!n'_s!(N-n_r)!(N-n'_s)!}{N!m!(n_r-m)!(n'_s-m)!(N-n_r-n'_s+m)!}

    is the expected value of :math:`\text{MI}(\boldsymbol x,\boldsymbol y)` if
    either partition has its labels randomly permuted, and :math:`\text{avg}` is the
    function corresponding to the parameter ``avg_methdod``.

    This algorithm runs in time :math:`O(N)` where :math:`N` is
    the length of :math:`\boldsymbol x` and :math:`\boldsymbol y`.

    @parallel@

        If ``adjusted == False``, the algorith will not run in parallel.

    Examples
    --------
    >>> x = np.random.randint(0, 10, 1000)
    >>> y = np.random.randint(0, 10, 1000)
    >>> gt.mutual_information(x, y)
    0.036350...

    References
    ----------
    .. [vinh_information_2009] Nguyen Xuan Vinh, Julien Epps, and James
       Bailey. 2009. “Information theoretic measures for clusterings comparison:
       is a correction for chance necessary?”, In Proceedings of the 26th Annual
       International Conference on Machine Learning (ICML '09). Association for
       Computing Machinery, New York, NY, USA,
       1073–1080. :doi:`10.1145/1553374.1553511`.

    """
    g = contingency_graph(x, y)
    nr = g.degree_property_map("out", g.ep.mrs)
    part = g.vp.partition.fa
    part = part[nr.fa > 0]
    nr = nr.fa[nr.fa > 0]
    mrs = g.ep.mrs.fa
    mrs = mrs[mrs > 0]
    N = mrs.sum()
    MI = (mrs * np.log(mrs)).sum() - (nr * np.log(nr)).sum()
    MI /= N
    MI += np.log(N)
    if adjusted:
        n1 = nr[part == 0].copy()
        n2 = nr[part == 1].copy()
        EMI = libinference.expected_MI(n1, n2)
        H1 = -(n1 * np.log(n1)).sum() / N + np.log(N)
        H2 = -(n2 * np.log(n2)).sum() / N + np.log(N)
        if avg_method == "max":
            avg = max((H1, H2))
        elif avg_method == "min":
            avg = min((H1, H2))
        elif avg_method == "arithmetic":
            avg = (H1 + H2) / 2
        elif avg_method == "geometric":
            avg = sqrt(H1 * H2)
        R = avg - EMI
        if R < 0:
            R = min((R, -np.finfo("float64").eps))
        else:
            R = max((R, np.finfo("float64").eps))
        MI = (MI - EMI)/ R
    elif norm:
        Hx = -((nr * np.log(nr))[part == 0]).sum() / N + np.log(N)
        Hy = -((nr * np.log(nr))[part == 1]).sum() / N + np.log(N)
        MI /= (Hx + Hy)/2
    return float(MI)

@_limit_args({"norm_method": ["symmetric", "asymmetric"]})
def reduced_mutual_information(x, y, norm=False, norm_method="asymmetric"):
    r"""Returns the reduced mutual information between two partitions.

    Parameters
    ----------
    x : iterable of ``int`` values
        First partition.
    y : iterable of ``int`` values
        Second partition.
    norm : ``bool`` (optional, default: ``False``)
        If ``True``, the result will be pseudo-normalized such that the returned
        value is one if the two partitions are identical.
    norm_method : ``"symmetric"`` or ``"asymmetric"`` (optional, default: ``"asymmetric"``)
        Method used for pseudo-normalization.

    Returns
    -------
    RMI : ``float``
        Reduced mutual information value.

    Notes
    -----

    The reduced mutual information (RMI) [newman_improved_2020]_ is defined as

    .. math::

        \text{RMI}(\boldsymbol x, \boldsymbol y) =
        \frac{1}{N}\left[\ln \frac{N!\prod_{rs}m_{rs}!}{\prod_rn_r!\prod_sn_s'!}
        -\ln\Omega(\boldsymbol n, \boldsymbol n')\right],

    with :math:`m_{rs}=\sum_i\delta_{x_i,r}\delta_{y_i,s}` being the contingency
    table between :math:`\boldsymbol x` and :math:`\boldsymbol y`, and
    :math:`n_r=\sum_sm_{rs}` and :math:`n'_s=\sum_rm_{rs}` are the group sizes
    in both partitions, and :math:`\Omega(\boldsymbol n, \boldsymbol n')` is the
    total number of contingency tables with fixed row and column sums.

    If ``norm == True``, the pseudo-normalized value is returned:

    .. math::

        \frac{\text{RMI}(\boldsymbol x, \boldsymbol y)}{\text{RMI}(\boldsymbol x, \boldsymbol x)}

    if ``norm_method == "asymmetric"``, or

    .. math::

        \frac{2\text{RMI}(\boldsymbol x, \boldsymbol y)}{\text{RMI}(\boldsymbol x, \boldsymbol x) + \text{RMI}(\boldsymbol y, \boldsymbol y)}

    if ``norm_method == "symmetric"``. In both cases the pseudo-normalized value
    will be unity if the two partitions are identical.

    .. warning::

        Note that both the pseudo-normalized and unormalized RMI values can be
        negative. In addition, the pseudo-normalized RMI can take values larger
        than unity for different partitions. These are issues with the
        definition of RMI, not bugs in this particular implementation.

    This algorithm runs in time :math:`O(N)` where :math:`N` is
    the length of :math:`\boldsymbol x` and :math:`\boldsymbol y`.

    Examples
    --------
    >>> x = np.random.randint(0, 10, 1000)
    >>> y = np.random.randint(0, 10, 1000)
    >>> gt.reduced_mutual_information(x, y)
    -0.069938...
    >>> x = [0, 1, 2, 3, 4, 5, 6]
    >>> y = [0, 0, 1, 0, 2, 3, 4]
    >>> gt.reduced_mutual_information(x, y, norm=True, norm_method="asymmetric")
    0.535938...
    >>> # Pseudo-normalized values larger than one are possible!
    >>> gt.reduced_mutual_information(x, y, norm=True, norm_method="symmetric")
    82.227299...
    >>> gt.reduced_mutual_information(x, x, norm=False)
    -0.162538...
    >>> gt.reduced_mutual_information(y, y, norm=False)
    0.160420...
    >>> gt.reduced_mutual_information(x, x, norm=True, norm_method="asymmetric")
    1.0
    >>> gt.reduced_mutual_information(x, x, norm=True, norm_method="symmetric")
    1.0
    >>> gt.reduced_mutual_information(y, y, norm=True, norm_method="asymmetric")
    1.0
    >>> gt.reduced_mutual_information(y, y, norm=True, norm_method="symmetric")
    1.0

    References
    ----------
    .. [newman_improved_2020] M. E. J. Newman, G. T. Cantwell and J.-G. Young,
       "Improved mutual information measure for classification and community
       detection", Phys. Rev. E, 101, 042304 (2020),
       :doi:`10.1103/PhysRevE.101.042304`, :arxiv:`1907.12581`

    """
    g = contingency_graph(x, y)
    nr = g.degree_property_map("out", g.ep.mrs)
    part = g.vp.partition.fa
    part = part[nr.fa > 0]
    nr = nr.fa[nr.fa > 0]
    mrs = g.ep.mrs.fa
    mrs = mrs[mrs > 0]
    N = mrs.sum()
    RMI = gammaln(N + 1) + gammaln(mrs + 1).sum() - gammaln(nr + 1).sum()
    lomega = libinference.log_omega(nr[part == 0], nr[part == 1])
    RMI -= lomega
    RMI /= N
    RMI = float(RMI)
    if norm:
        if norm_method == "asymmetric":
            RMI /= reduced_mutual_information(x, x, norm=False)
        else:
            RMI /= (reduced_mutual_information(x, x, norm=False) +
                    reduced_mutual_information(y, y, norm=False)) / 2
    return RMI
